The moment of force is the magnitude of the force multiplied by the perpendicular distance from the axis to the force.
hinge
• The product of the force and the perpendicular distance from the axis is known as the moment of force.
• The perpendicular distance is taken from where you exert the force to where the fulcrum is.
• The force produced at the other end is known as the load. • Moments are scalar and have units N m.
Doors act as levers: you apply a force and the fulcrum is the hinge. Have you tried pushing a door very close to the hinge, as in Fig. 6.3b? This reduces the moment and makes it very difficult!
Moment of a force M = Fd
M = moment of force (N m), F = force (N), d = distance from fulcrum (m) F d d F
Moments can be clockwise or anticlockwise. In order to work out which moment is which, picture the way a ruler balanced on a fulcrum would turn if you applied a force at one end (Fig. 6.4).
a b
FIG. 6.3 It is difficult to push a door close to the hinge as the moment of force is low
3 m 80 N 6 m 40 N
• •
If you push down on the right, it will turn clockwise (clockwise moment).
If you push down on the left, it will turn anticlockwise (anticlockwise moment).
In order to work out which way a body will rotate and with how much turning effect:
• •
add up all the clockwise moments and all the anticlockwise moments separately
then subtract the smaller amount and the result is the net moment of force.
This means moments can be added or subtracted algebraically. So, for example, in Fig. 6.4:
anticlockwise clockwise
FIG. 6.4 Moments can be clockwise or anticlockwise
• anticlockwise moments = (80)(3) = 240 N m • clockwise moments = (40)(6) = 240 N m
Because the clockwise moments equal the anticlockwise moments, the bar is in equilibrium.
Conditions for equilibrium
Any body that is in a state of rest or constant velocity is in equilibrium. This means it could be in:
• static equilibrium (not moving) • dynamic equilibrium (moving but not accelerating).
